--- rpl/lapack/lapack/dlarzt.f 2011/07/22 07:38:07 1.8 +++ rpl/lapack/lapack/dlarzt.f 2011/11/21 20:42:58 1.9 @@ -1,9 +1,194 @@ +*> \brief \b DLARZT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARZT + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARZT forms the triangular factor T of a real block reflector +*> H of order > n, which is defined as a product of k elementary +*> reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**T +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**T * T * V +*> +*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise (not supported yet) +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in,out] V +*> \verbatim +*> V is DOUBLE PRECISION array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is DOUBLE PRECISION array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERcomputational +* +*> \par Contributors: +* ================== +*> +*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored; the corresponding +*> array elements are modified but restored on exit. The rest of the +*> array is not used. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> ______V_____ +*> ( v1 v2 v3 ) / \ +*> ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 ) +*> V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 ) +*> ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 ) +*> ( v1 v2 v3 ) +*> . . . +*> . . . +*> 1 . . +*> 1 . +*> 1 +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> ______V_____ +*> 1 / \ +*> . 1 ( 1 . . . . v1 v1 v1 v1 v1 ) +*> . . 1 ( . 1 . . . v2 v2 v2 v2 v2 ) +*> . . . ( . . 1 . . v3 v3 v3 v3 v3 ) +*> . . . +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> V = ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> \endverbatim +*> +* ===================================================================== SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) * -* -- LAPACK routine (version 3.3.1) -- +* -- LAPACK computational routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -- April 2011 -- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIRECT, STOREV @@ -13,112 +198,6 @@ DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) * .. * -* Purpose -* ======= -* -* DLARZT forms the triangular factor T of a real block reflector -* H of order > n, which is defined as a product of k elementary -* reflectors. -* -* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; -* -* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. -* -* If STOREV = 'C', the vector which defines the elementary reflector -* H(i) is stored in the i-th column of the array V, and -* -* H = I - V * T * V**T -* -* If STOREV = 'R', the vector which defines the elementary reflector -* H(i) is stored in the i-th row of the array V, and -* -* H = I - V**T * T * V -* -* Currently, only STOREV = 'R' and DIRECT = 'B' are supported. -* -* Arguments -* ========= -* -* DIRECT (input) CHARACTER*1 -* Specifies the order in which the elementary reflectors are -* multiplied to form the block reflector: -* = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet) -* = 'B': H = H(k) . . . H(2) H(1) (Backward) -* -* STOREV (input) CHARACTER*1 -* Specifies how the vectors which define the elementary -* reflectors are stored (see also Further Details): -* = 'C': columnwise (not supported yet) -* = 'R': rowwise -* -* N (input) INTEGER -* The order of the block reflector H. N >= 0. -* -* K (input) INTEGER -* The order of the triangular factor T (= the number of -* elementary reflectors). K >= 1. -* -* V (input/output) DOUBLE PRECISION array, dimension -* (LDV,K) if STOREV = 'C' -* (LDV,N) if STOREV = 'R' -* The matrix V. See further details. -* -* LDV (input) INTEGER -* The leading dimension of the array V. -* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. -* -* TAU (input) DOUBLE PRECISION array, dimension (K) -* TAU(i) must contain the scalar factor of the elementary -* reflector H(i). -* -* T (output) DOUBLE PRECISION array, dimension (LDT,K) -* The k by k triangular factor T of the block reflector. -* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is -* lower triangular. The rest of the array is not used. -* -* LDT (input) INTEGER -* The leading dimension of the array T. LDT >= K. -* -* Further Details -* =============== -* -* Based on contributions by -* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA -* -* The shape of the matrix V and the storage of the vectors which define -* the H(i) is best illustrated by the following example with n = 5 and -* k = 3. The elements equal to 1 are not stored; the corresponding -* array elements are modified but restored on exit. The rest of the -* array is not used. -* -* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': -* -* ______V_____ -* ( v1 v2 v3 ) / \ -* ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 ) -* V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 ) -* ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 ) -* ( v1 v2 v3 ) -* . . . -* . . . -* 1 . . -* 1 . -* 1 -* -* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': -* -* ______V_____ -* 1 / \ -* . 1 ( 1 . . . . v1 v1 v1 v1 v1 ) -* . . 1 ( . 1 . . . v2 v2 v2 v2 v2 ) -* . . . ( . . 1 . . v3 v3 v3 v3 v3 ) -* . . . -* ( v1 v2 v3 ) -* ( v1 v2 v3 ) -* V = ( v1 v2 v3 ) -* ( v1 v2 v3 ) -* ( v1 v2 v3 ) -* * ===================================================================== * * .. Parameters ..